2.2: IfThen Statements
Rube Goldberg was a cartoonist in the 1940s who drew crazy inventions to do very simple things. The invention below has a series of smaller tasks that leads to the machine wiping the man’s face with a napkin.
Write a series of ifthen statements to that would caption this cartoon, from \begin{align*}A\end{align*}
Watch This
CK12 Foundation: Chapter2IfThenStatementsA
James Sousa: IfThen Statements and Converses
Guidance
A conditional statement (also called an IfThen Statement) is a statement with a hypothesis followed by a conclusion. Another way to define a conditional statement is to say, “If this happens, then that will happen.”
The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement. The conclusion is the result of a hypothesis. Keep in mind that conditional statements might not always be written in the “ifthen” form. Here are a few examples.
 Statement 1: If you work overtime, then you’ll be paid timeandahalf.
 Statement 2: I’ll wash the car if the weather is nice.

Statement 3: If 2 divides evenly into \begin{align*}x\end{align*}
x , then \begin{align*}x\end{align*}x is an even number.
 Statement 4: I’ll be a millionaire when I win monopoly.
 Statement 5: All equiangular triangles are equilateral.
Statements 1 and 3 are written in the “ifthen” form. The hypothesis of Statement 1 is “you work overtime.” The conclusion is “you’ll be paid timeandahalf.” So, if Sarah works overtime, then what will happen? From Statement 1, we can conclude that she will be paid timeandahalf. If 2 goes evenly into 16, what can you conclude? From Statement 3, we know that 16 must be an even number. Statement 2 has the hypothesis after the conclusion. Even though the word “then” is not there, the statement can be rewritten as: If the weather is nice, then I’ll wash the car. If the word “if” is in the middle of a conditional statement, the hypothesis is always after it. Statement 4 uses the word “when” instead of “if.” It should be treated like Statement 2, so it can be written as: If I win monopoly, then I will be a millionaire. In Statement 5 “if” and “then” are not there, but can be rewritten as: If a triangle is equiangular, then it is equilateral.
Example A
Rewrite the following statement in ifthen form: All students like geometry.
Rewritten in ifthen form, this statement would be if you are a student, then you like geometry.
Example B
Identify the hypothesis and the conclusion of the statement: Bob will go to the store if Anne tells him what to buy.
First, rewrite in ifthen form. If Anne tells Bob what to buy, then Bob will go to the store. The hypothesis is Anne tells Bob what to buy because this has to come first. The conclusion, or result, is Bob will go to the store.
Example C
Identify the hypothesis and the conclusion of the statement: I bring my umbrella when it is raining.
Rewrite in ifthen form, considering what causes what. In this situation, it is the rain that causes me to bring an umbrella (not bringing an umbrella that causes rain). If it is raining, then I bring my umbrella. The hypothesis is it is raining and the conclusion is I bring my umbrella.
Watch this video for help with the Examples above.
CK12 Foundation: Chapter2IfThenStatementsB
Concept Problem Revisited
The conditional statements are as follows:
\begin{align*}A \rightarrow B\end{align*}
\begin{align*}B \rightarrow C\end{align*}
\begin{align*}C \rightarrow D\end{align*}
\begin{align*}D \rightarrow E\end{align*}
\begin{align*}E \rightarrow F\end{align*}
\begin{align*}F \rightarrow G\end{align*}
\begin{align*}G \rightarrow H\end{align*}
\begin{align*}H \rightarrow I\end{align*}
\begin{align*}I \rightarrow J\end{align*}
\begin{align*}J \rightarrow K\end{align*}
\begin{align*}K \rightarrow L\end{align*}
\begin{align*}L \rightarrow M\end{align*}
This is a very complicated contraption used to wipe a man’s face. Purdue University liked these cartoons so much, that they started the Rube Goldberg Contest in 1949. This past year, the task was to pump hand sanitizer into someone’s hand in no less than 20 steps.
Purdue University: Purdue team smashes Rube Goldberg world record
Vocabulary
A conditional statement (also called an IfThen Statement) is a statement with a hypothesis followed by a conclusion. The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement.
Guided Practice
First rewrite in ifthen form, then determine the hypothesis and conclusion.
1. Sally eats a snack if she is hungry.
2. The angles in a triangle add up to 180 degrees.
3. 2012 is a leap year.
Answers:
1. In ifthen form, the statement is If Sally is hungry, then she eats a snack. The hypothesis is Sally is hungry and the conclusion is she eats a snack.
2. In ifthen form, the statement is If a shape is a triangle, then its angles add up to 180 degrees. The hypothesis is a shape is a triangle and the conclusion is its angles add up to 180 degrees.
3. In ifthen form, the statement is If it is 2012, then it is a leap year. The hypothesis is it is 2012 and the conclusion is it is a leap year.
Practice
For questions 16, determine the hypothesis and the conclusion.
 If 5 divides evenly into \begin{align*}x\end{align*}
x , then \begin{align*}x\end{align*}x ends in 0 or 5.  If a triangle has three congruent sides, it is an equilateral triangle.
 Three points are coplanar if they all lie in the same plane.
 If \begin{align*}x =3\end{align*}
x=3 , then \begin{align*}x^2=9\end{align*}x2=9 .  If you take yoga, then you are relaxed.
 All baseball players wear hats.
 I'll learn how to drive when I am 16 years old.
 If you do your homework, then you can watch TV.
 Alternate interior angles are congruent if lines are parallel.
 All kids like ice cream.
Rewrite each statement in ifthen form.
 Susie eats pizza every Thursday.
 Raychel always completes her homework.
 Alex goes to school every weekday.
 All students have a math class.
 Squares have right angles.
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Image Attributions
Here you'll learn how to rewrite statements in ifthen form and determine the hypothesis and conclusion.